@article{BRZOZOWSKI201413,
    Abstract = {We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call ``{\'a}tomaton'', whose states are the ``atoms'' of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing the {\'a}tomaton, and prove that it is isomorphic to the reverse automaton of the minimal deterministic finite automaton (DFA) of the reverse language. We study ``atomic'' NFAs in which the right language of every state is a union of atoms. We generalize Brzozowski's double-reversal method for minimizing a deterministic finite automaton (DFA), showing that the result of applying the subset construction to an NFA is a minimal DFA if and only if the reverse of the NFA is atomic. We prove that Sengoku's claim that his method always finds a minimal NFA is false.},
    Author = {Brzozowski, Janusz and Tamm, Hellis},
    File = {Theory of átomata - 1-s2.0-S0304397514002953-main - x - x.pdf},
    ISSN = {0304-3975},
    Journal = {Theoretical Computer Science},
    Keywords = {Atom, Atomic NFA, {\'A}tomaton, Left quotient, Minimization by double reversal, NFA, Regular language},
    Pages = {13-27},
    Title = {Theory of {\'a}tomata},
    URL = {https://www.sciencedirect.com/science/article/pii/S0304397514002953},
    Volume = {539},
    Year = {2014},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0304397514002953},
    bdsk-url-2 = {https://doi.org/10.1016/j.tcs.2014.04.016},
    date-added = {2021-03-18 09:05:50 +0100},
    date-modified = {2021-03-18 09:05:50 +0100},
    doi = {10.1016/j.tcs.2014.04.016}
}

@article{BRZOZOWSKI201413, Abstract = {We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call {\'a}tomaton'', whose states are theatoms'' of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing the {\'a}tomaton, and prove that it is isomorphic to the reverse automaton of the minimal deterministic finite automaton (DFA) of the reverse language. We study ``atomic'' NFAs in which the right language of every state is a union of atoms. We generalize Brzozowski's double-reversal method for minimizing a deterministic finite automaton (DFA), showing that the result of applying the subset construction to an NFA is a minimal DFA if and only if the reverse of the NFA is atomic. We prove that Sengoku's claim that his method always finds a minimal NFA is false.}, Author = {Brzozowski, Janusz and Tamm, Hellis}, File = {Theory of átomata - 1-s2.0-S0304397514002953-main - x - x.pdf}, ISSN = {0304-3975}, Journal = {Theoretical Computer Science}, Keywords = {Atom, Atomic NFA, {\'A}tomaton, Left quotient, Minimization by double reversal, NFA, Regular language}, Pages = {13-27}, Title = {Theory of {\'a}tomata}, URL = {https://www.sciencedirect.com/science/article/pii/S0304397514002953}, Volume = {539}, Year = {2014}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0304397514002953}, bdsk-url-2 = {https://doi.org/10.1016/j.tcs.2014.04.016}, date-added = {2021-03-18 09:05:50 +0100}, date-modified = {2021-03-18 09:05:50 +0100}, doi = {10.1016/j.tcs.2014.04.016} }